Speaking to BBC News, Major General James Everard, Assistant Chief of the General Staff, said:
We owe a huge apology to the families involved and those who will now be feeling stressful even if it doesn't affect them.
These were just tissue samples that we had failed to recover post-inquest and deal with in line with the families' wishes.
It's a failure of process, nothing more than that, but we absolutely recognise this will cause distress and we're deeply sorry."
More top news
Becky Watts allegedly told a friend that Nathan Matthews, who is on trial for her murder, described how he would kill her in 2013.
Five people have been arrested after clashes between football fans and police before a Swindon - Oxford match on Tuesday night.
Nathan Matthews, the step-brother of Becky Watts, has admitted to killing the teen - but denies he murder her.